Moments of claims in a Markovian environment

Bara Kim, Hwa Sung Kim

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.

Original languageEnglish
Pages (from-to)485-497
Number of pages13
JournalInsurance: Mathematics and Economics
Volume40
Issue number3
DOIs
Publication statusPublished - 2007 May 1

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Moment
Laplace-Stieltjes Transform
System of Differential Equations
Differential equation
Numerical Examples
Differential equations
Laplace transform
Business risk

Keywords

  • Circumstance process
  • Discounted aggregate claims
  • Laplace-Stieltjes transform
  • Moments

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Economics and Econometrics

Cite this

Moments of claims in a Markovian environment. / Kim, Bara; Kim, Hwa Sung.

In: Insurance: Mathematics and Economics, Vol. 40, No. 3, 01.05.2007, p. 485-497.

Research output: Contribution to journalArticle

Kim, Bara ; Kim, Hwa Sung. / Moments of claims in a Markovian environment. In: Insurance: Mathematics and Economics. 2007 ; Vol. 40, No. 3. pp. 485-497.
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